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Labelling of triangulation

Source: Austrian-Polish 1985, Problem 8

July 5, 2015
combinatoricstriangulationpolygon

Problem Statement

A convex nn-gon A0A1…An−1A_0A_1\dots A_{n-1} has been partitioned into n−2n-2 triangles by certain diagonals not intersecting inside the nn-gon. Prove that these triangles can be labeled △1,△2,…,△n−2\triangle_1,\triangle_2,\dots,\triangle_{n-2} in such a way that AiA_i is a vertex of △i\triangle_i, for i=1,2,…,n−2i=1,2,\dots,n-2. Find the number of all such labellings.
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